feat: add find_missing_number function to bit_manipulation

[AliAlimohammadi]

Description

Adds a new function find_missing_number to the bit_manipulation module that finds the missing number in an array of consecutive integers.

Algorithm

Uses XOR bitwise operation to efficiently find the missing number:

1. Finds the minimum and maximum values in the array
2. XORs all expected numbers in the range [min, max] with actual numbers
3. Since a ^ a = 0, all present numbers cancel out, leaving only the missing number

Implementation Details

• Time Complexity: $O(n)$ - single pass to find min/max, then $O(n)$ for XOR operations
• Space Complexity: $O(1)$ - constant extra space
• Works with:
  • Unordered arrays
  • Negative numbers
  • Mixed positive and negative ranges
• Proper error handling for edge cases (empty array, single element)

Examples

find_missing_number(&[0, 1, 3, 4]) // Returns 2
find_missing_number(&[-4, -3, -1, 0]) // Returns -2
find_missing_number(&[4, 3, 1, 0]) // Returns 2 (works with unordered)

Testing

• ✅ All existing tests pass
• ✅ New tests added for:
  • Missing number in middle of sequence
  • Unordered arrays
  • Negative numbers
  • Mixed negative and positive numbers
  • Edge cases (empty array, single element, two elements)
  • Large ranges
  • Missing at boundaries

Checklist

• Code follows Rust style guidelines (cargo fmt)
• Passes clippy lints (cargo clippy)
• All tests pass (cargo test)
• Documentation includes examples
• Function is properly exported in module
• Error handling implemented for invalid inputs
• Works with negative numbers and unordered arrays

[codecov-commenter]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 95.67%. Comparing base (7a261d7) to head (26c690f).

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #974      +/-   ##
==========================================
- Coverage   95.71%   95.67%   -0.04%     
==========================================
  Files         346      347       +1     
  Lines       22608    22665      +57     
==========================================
+ Hits        21639    21685      +46     
- Misses        969      980      +11     

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[AliAlimohammadi]

@siriak, this is ready to be merged.